June 18, 2007
Commentary on the New Hazard
Groups
CAS Spring Meeting
Jose Couret
Orlando
Outline
Motivation
Gauging the Improvement
Excess Loss Factors by Class
Conclusion
1
Motivation
Motivation
Development of New Hazard Groups
 Old Hazard Group Mapping
– Until recently, hundreds of class codes were condensed into 4
hazard groups--of which hazard groups II and III contained 95% of
the exposure.
 New Hazard Group Mapping
– The number of hazard groups has increased to seven (from four)
under NCCI’s B-1403 filing.
– The new hazard groups are a significant improvement.
3
Motivation
An ELF is a Weighted Average of the ELFs by Injury Type
Fatal
PT
Major
Minor
TT
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
$0
$100,000
$200,000
$300,000
$400,000
$500,000
$600,000
$700,000
$800,000
$900,000
$1,000,000
$1,100,000
$1,200,000
$1,300,000
$1,400,000
$1,500,000
4
Gauging the Improvement
Gauging the Improvement
Discussion
 A key element of the excess percentage is the frequency of loss by
injury type. Fatalities and permanent disabilities cost more than other
injury types; so when they have high relative frequency, more of the
claims cost arises from large losses.
 Relative Frequency = claim count for the injury type divided by the
claim count for temporary total.
 Relative frequency for the more serious injury types should increase as
one moves from a lower hazard group to a higher hazard group.
– Fatal
– Permanent Total
– Major Permanent Partial
6
Gauging the Improvement
Relative Frequency by Hazard Group and Injury Type
HG
Fatal:TT
PT:TT
Major:TT
Minor:TT
TT:TT
MO:TT
A
B
C
D
E
F
G
0.001
0.002
0.003
0.004
0.005
0.007
0.013
0.002
0.004
0.005
0.005
0.006
0.009
0.016
0.052
0.083
0.099
0.118
0.151
0.198
0.249
0.350
0.392
0.395
0.387
0.371
0.344
0.394
1.000
1.000
1.000
1.000
1.000
1.000
1.000
5.663
5.641
5.050
4.590
3.983
2.970
2.992
All
0.004
0.006
0.122
0.380
1.000
4.615
Note: Undeveloped, adjusted to Countrywide Level
7
Gauging the Improvement
Relative Frequency by Hazard Group and Injury Type
Classes Formerly in Hazard Group II
HG
Fatal:TT
PT:TT
Major:TT
Minor:TT
TT:TT
MO:TT
A
B
C
D
E
F
G
0.001
0.002
0.003
0.003
0.003
0.006
-
0.002
0.004
0.004
0.005
0.004
0.007
-
0.049
0.084
0.096
0.112
0.091
0.119
-
0.342
0.397
0.393
0.438
0.297
0.397
-
1.000
1.000
1.000
1.000
1.000
1.000
-
5.750
5.704
5.032
5.239
3.866
3.728
-
All
0.002
0.004
0.089
0.391
1.000
5.285
Note: Undeveloped, adjusted to Countrywide Level
8
Gauging the Improvement
Relative Frequency by Hazard Group and Injury Type
Classes Formerly in Hazard Group III
HG
Fatal:TT
PT:TT
Major:TT
Minor:TT
TT:TT
MO:TT
A
B
C
D
E
F
G
0.002
0.004
0.004
0.006
0.007
0.011
0.003
0.005
0.005
0.007
0.009
0.013
0.062
0.123
0.122
0.158
0.198
0.227
0.268
0.407
0.346
0.380
0.340
0.396
1.000
1.000
1.000
1.000
1.000
1.000
5.371
5.153
4.076
3.998
2.936
2.625
All
0.006
0.007
0.164
0.364
1.000
3.730
Note: Undeveloped, adjusted to Countrywide Level
9
Gauging the Improvement
Fatal Frequencies– Within and Between Hazard Groups
A
80
40
0
B
80
Hazard Group
means are very
different.
40
0
C
80
40
0
h
g
7
D
80
Is the variation
within hazard
groups significant?
40
0
E
80
40
0
F
80
40
0
G
80
40
0
0
0. 01725613
0. 03451226
0. 05176838
0. 06902451
0. 08628064
0. 10353677
Fat al : TT
10
Gauging the Improvement
PT Frequencies– Within and Between Hazard Groups
A
80
40
0
B
80
40
0
C
80
40
0
h
g
7
D
80
40
0
E
80
40
0
F
80
40
0
G
80
40
0
0
0. 00810585 0. 01621169 0. 02431754 0. 03242339 0. 04052923 0. 04863508 0. 05674093
PT : T T
11
Gauging the Improvement
Major Frequencies– Within and Between Hazard Groups
A
30
15
0
B
30
15
0
C
30
15
0
h
g
7
D
30
15
0
E
30
15
0
F
30
15
0
G
30
15
0
0. 014 0. 054 0. 094 0. 134 0. 174 0. 214 0. 254 0. 294 0. 334 0. 374 0. 414 0. 454 0. 494 0. 534
Ma j o r : T T
12
Gauging the Improvement
Performance Testing with A Holdout Sample

For each injury type, calculated relative frequency for the even
reports (2, 4, 6) and used these to predict the odd reports (3, 5, 7).
Discarded greenest year of data (first report).

Estimates are expressed as relativities to the all-class relative
frequencies.

Three methods used to predict holdout period outcome:
1. No hazard group method
2. Old 4-hazard group method
3. New 7-hazard group method

Note: statistical procedure used to eliminate state differentials.
13
Gauging the Improvement
Performance Testing with A Holdout Sample
Fatal Claims
(1)
Approx
7x greater
Hazard
Group
A
B
C
D
E
F
G
(2)
(3)
(4)
(5)
Holdout
Period
Relativity
0.43643
0.48555
0.68370
1.05510
1.30104
1.85093
2.95338
Prediction
Without
HG
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
Prediction
Based On
Old 4-HG
0.61064
0.63025
0.73183
1.09209
1.35524
1.47003
2.39305
Prediction
Based On
New 7-HG
0.39589
0.49673
0.71623
0.91244
1.33699
1.83257
3.16405
1.00000
1.00000
5.31575
1.00000
0.51697
1.00000
0.06919
Mean
SSE
Hold-out period relativities we
are trying to predict.
Clearly, predictions based on new 7-HG averages from
even years more closely track holdout period results.
New 7-HG predictions yield lowest sum of squared errors.
14
Gauging the Improvement
Performance Testing with A Holdout Sample
Permanent Total claims
(1)
Hazard
Group
A
B
C
D
E
F
G
Mean
SSE
(2)
(3)
(4)
(5)
Holdout
Period
Relativity
0.50791
0.78888
0.82907
0.92482
1.05933
1.59147
2.46731
Prediction
Without
HG
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
Prediction
Based On
Old 4-HG
0.77136
0.79082
0.85531
1.04844
1.18931
1.25555
1.85357
Prediction
Based On
New 7-HG
0.50791
0.74260
0.85528
0.90114
1.15000
1.56268
2.24219
1.00000
1.00000
2.82796
1.00000
0.59179
1.00000
0.06312
New 7-HG predictions yield lowest sum of squared errors.
15
Gauging the Improvement
Performance Testing with A Holdout Sample
Major Permanent Partial Claims
(1)
Hazard
Group
A
B
C
D
E
F
G
Mean
SSE
(2)
(3)
(4)
(5)
Holdout
Period
Relativity
0.48293
0.73543
0.85706
0.95867
1.20489
1.56231
1.77769
Prediction
Without
HG
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
Prediction
Based On
Old 4-HG
0.75709
0.76893
0.83503
1.07328
1.24724
1.30813
1.58653
Prediction
Based On
New 7-HG
0.45373
0.74128
0.83793
0.97761
1.21946
1.56371
1.81744
1.00000
1.00000
1.32248
1.00000
0.19285
1.00000
0.00341
New 7-HG predictions yield lowest sum of squared errors.
16
Gauging the Improvement
Comments
 Testing suggests that the new hazard groups are superior to the old.
 There is great value in having seven sets of benchmark excess loss
factors that do not “cross over”.
 New hazard groups are still sufficiently heterogeneous for a correlated
credibility approach to add value. Even then, the hazard group
estimate can serve as the complement of credibility.
 May be impractical for bureaus to support ELFs by class. Individual
insurers can derive their own credits and debits to adjust hazard group
ELFs to class level.
17
Excess Loss Factors by Class
Excess Loss Factors by Class
Relative Permanent Total (PT) Frequency by Class Code
50
40
P
e
r
c
e
n
t
30
20
10
0
0. 25
0. 5
0. 75
1
1. 25
1. 5
1. 75
P T Re l a t i v i t y
2
2. 25
( Cr e d i b i l i t y
2. 5
2. 75
Ad j u s t e d ,
3
Be f o r e
3. 25
3. 5
3. 75
4
4. 25
Ca p s )
19
Excess Loss Factors by Class
Sample State, $4m XS $1M
40
A
20
0
40
B
20
0
H
a
z
a
r
d
40
C
20
0
40
D
G
r
o
u
p
20
0
40
E
20
0
40
F
20
0
40
G
20
0
0. 02775
0. 03675
0. 04575
0. 05475
0. 06375
Layer
Loss
0. 07275
Co s t
0. 08175
0. 09075
0. 09975
0. 10875
( %)
20
Excess Loss Factors by Class
Sample State, $5m XS $5M
40
A
20
0
40
B
20
0
H
a
z
a
r
d
40
C
20
0
40
D
G
r
o
u
p
20
0
40
E
20
0
40
F
20
0
40
G
20
0
0. 001875 0. 003625 0. 005375 0. 007125 0. 008875 0. 010625 0. 012375 0. 014125 0. 015875 0. 017625
Layer
Loss
Co s t
( %)
21
Excess Loss Factors by Class
Credibility Procedure Yields Modest Reduction in Sum of Squared Errors
Sum of Squared Prediction Errors by Injury Type
(1)
Injury
Type
Fatal
PT
Major PP
Minor PP
Med. Only
(2)
Prediction
Based on
HG
43.6
34.7
1,425.0
6,756.9
417,260.8
(3)
Prediction
Based on
Raw Even
65.2
83.6
2,201.7
10,360.3
434,837.9
(4)
Prediction
Based on
Cred. Proc.
43.5
34.6
1,405.6
6,558.0
351,270.8
22
Excess Loss Factors by Class
Quintiles Test
 Utilizing a variation on NCCI’s “Quintiles Test” to measure model
performance
– Approach used to test Experience Rating Plan
 Hazard grouping approximation works best when all classes in a
Hazard Group
– have the same relative frequency of injuries
– same composition of loss by injury type
 Our goal: determine if by-class approach improves prediction of injury
type relative frequency.
23
Excess Loss Factors by Class
Quintiles Test Methodology
 Discard greenest year of data (first report)
 For each injury type, calculated relative frequency relativities (to the
hazard group average) from the even reports (2, 4, 6).
– Used these to predict the odd reports (3, 5, 7)
 Classes within a HG are sorted by credibility-weighted relativity and
aggregated into five groups of roughly equal size.
– Groupings were created so that the number of TT claim counts in
each quintile is roughly equal.
– The lowest 20% of the class relativities belong to the risks in the first
quintile, the next 20% to the second quintile, etc.
24
Excess Loss Factors by Class
Observations
Hazard Group D, Permanent Total Claims
(1)
Quintile
1
2
3
4
5
Mean
SSE
(2)
(3)
(4)
(5)
Prediction Based
Prediction Based Prediction Based
on Cred.
Odd Relativity
on HG
on Raw Even
Procedure
0.4951
1.0000
0.3065
0.5648
0.8634
1.0000
0.4260
0.8732
0.9861
1.0000
0.7513
1.0000
1.1269
1.0000
1.3473
1.1038
1.5215
1.0000
2.1547
1.4519
1.0000
1.0000
0.5618
1.0000
0.7315
Column (2), what we are trying to predict,
represents the average relative frequency for
the classes in the quintile divided by the
corresponding estimate for all of HG D. For
example, the relative frequency of PT claims
(as a ratio to TT) for the classes within the first
quintile was about half of the HG average.
1.0000
0.0105
Upwardly sloping relativities are desirable; indicate
the credibility procedure tended to identify class
difference in relative PT frequency.
25
Excess Loss Factors by Class
Observations (continued)
 Goal is to predict the Column (2) frequency relativity for each quintile.
Column (3) is a prediction based on the HG average. All entries equal
to unity – by assumption every quintile has the HG D relative frequency
for PT claims.
 The predictions in Column (4) are based on raw class relativities
observed for the even years. For example, the classes in the fifth
quintile had an even-year relative PT frequency that was 215% of the
HG average.
 The Column (5) predictions were derived using the multi-dimensional
credibility procedure.
 Again, the quintiles are ranked by credibility weighted class relativity,
not raw relativity.
26
Excess Loss Factors by Class
Observations (continued)
Hazard Group D, Permanent Total Claims
(1)
Approx
3x greater
(2)
(3)
Quintile
1
2
3
4
5
Odd Relativity
0.4951
0.8634
0.9861
1.1269
1.5215
Prediction
Based on HG
1.0000
1.0000
1.0000
1.0000
1.0000
Mean
SSE
1.0000
Actual Odd year relativities we
are trying to predict. Classes
in highest quintile 3x more
likely to have a PT claim
1.0000
0.5618
(4)
(5)
Prediction Based
Prediction Based
on Cred.
on Raw Even
Procedure
0.3065
0.5648
0.4260
0.8732
0.7513
1.0000
1.3473
1.1038
2.1547
1.4519
1.0000
0.7315
Flat relativities significantly
underestimate PT frequency for
classes in higher quintiles and
overestimate lower quintiles
1.0000
0.0105
Prediction based on
Even years gives too
much credibility to
historical experience
There is significant variability of PT frequency within Hazard Group D
27
Excess Loss Factors by Class
Sum of Squared Prediction Errors by Hazard Group and Injury Type
Prediction
Based on
HG
0.13227
0.32630
0.83604
0.97498
0.49691
0.39060
0.55650
Prediction
Based on
Raw Even
0.94431
1.79940
1.39413
0.87260
1.44023
1.35362
1.23015
Prediction
Based on
Cred. Proc.
0.18952
0.05637
0.03376
0.12111
0.05096
0.07280
0.06035
HG
A
B
C
D
E
F
G
Injury
Type
Fatal
Fatal
Fatal
Fatal
Fatal
Fatal
Fatal
A
B
C
D
E
F
G
PT
PT
PT
PT
PT
PT
PT
0.03941
0.38273
0.56175
0.56183
0.73195
0.56872
1.09139
1.94151
1.34145
0.55609
0.73151
0.82350
0.53817
0.52326
0.57993
0.11044
0.01180
0.01053
0.07050
0.01812
0.07946
A
B
C
D
E
F
G
Major
Major
Major
Major
Major
Major
Major
0.58481
0.33888
0.38001
0.18900
0.28775
0.32418
0.58518
0.01988
0.03729
0.04108
0.03928
0.07476
0.04703
0.14046
0.05079
0.00870
0.00738
0.01850
0.01030
0.01781
0.00538
Supports severity differentials
by hazard group for permanent
partial losses.
Thinking in R2 terms, the class relativities could be said to "explain" 98% of the
"between quintiles” variance for PT/HG D. This is not actually a regression, but the
statistic is still impressive by real-life actuarial standards. The use of class relativities
dramatically improves the class frequency by injury type estimation.
28
Conclusion
Conclusion
 The new hazard groups are superior to the old.
 There is great value in having excess loss factors that do
not “cross over”.
 A correlated credibility approach can be used to calculate
indicated credits/debits to the hazard group ELFs. The
actual credit/debit must incorporate underwriting judgment.
30